Fourth-, Fifth-, Sixth-Order Linear Differential Equations (LDEs) via Homotopy Perturbation Method Using Laplace Transform

2018 ◽  
pp. 679-698
Author(s):  
Rajnee Tripathi ◽  
Hradyesh Kumar Mishra
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Linear Differential Equations ◽  
Sixth Order ◽  
Order Linear ◽  
Homotopy Perturbation ◽  
Linear Differential

scholarly journals Hybridization of homotopy perturbation method and Laplace transformation for the partial differential equations

2017 ◽  
Vol 21 (4) ◽  
pp. 1843-1846 ◽  
Author(s):  
Zhen-Jiang Liu ◽  
Magaji Adamu ◽  
Enoch Suleiman ◽  
Ji-Huan He
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Analytical Solutions ◽  
Laplace Transformation ◽  
Homotopy Perturbation Method ◽  
Solution Process ◽  
Initial Approximation ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Linear Differential

Homotopy perturbation method is combined with Laplace transformation to obtain approximate analytical solutions of non-linear differential equations. An example is given to elucidate the solution process and confirm reliability of the method. The result indicates superiority of the method over the conventional homotopy perturbation method due its flexibility in choosing its initial approximation.

Application of New Homotopy Perturbation Method for Solving Partial Differential Equations

2018 ◽  
Vol 15 (2) ◽  
pp. 500-508 ◽  
Author(s):  
Musa R. Gad-Allah ◽  
Tarig M. Elzaki
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Novel Technique ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
Linear Differential

In this paper, a novel technique, that is to read, the New Homotopy Perturbation Method (NHPM) is utilized for solving a linear and non-linear differential equations and integral equations. The two most important steps in the application of the new homotopy perturbation method are to invent a suitable homotopy equation and to choose a suitable initial conditions. Comparing between the effects of the method (NHPM), is given exact solution, and the method (HPM), is given approximate solution, in this paper, we make some instances are provided to prove the ability of the method (NHPM). Show that the method (NHPM) is valid and effective, easy and accurate in solving linear and nonlinear differential equations, compared with the Homotopy Perturbation Method (HPM).

scholarly journals Analisis Solusi Model Rangkaian Listrik Menggunakan Metode Transformasi Laplace Modifikasi

2020 ◽  
Vol 8 (1) ◽  
pp. 21
Author(s):  
Fitriana Minggani
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Integral Transformation ◽  
Electrical Circuit ◽  
Second Order ◽  
Linear Differential Equations ◽  
Electric Circuits ◽  
Order Linear ◽  
Limit Value ◽  
Linear Differential

AbstractLaplace transform is one typr of integral transformation that allows to be used to solve homogeneous and non- homogeneous second order linear differential equations. Laplace transform modification is obtained by adding coefficients through the corresponding variables in the Laplace transform equation expressed in term of =   with   that a transformation kernel function and  is a transformation variable for . There are several applications of differential equations, one of which is the electrical circuit model. The prblem that often becomes an obstacle is when encountering a limit value problem. This paper aims to obtain the solution of linear differential equations in a simple electric circuits (RLC) model connected in series, using a modified Laplace transform. The results of this study provide solutions in the form of  second order linear differential equations: Keywords: electrical circuits, Laplace transform modifications, second order linear differential equations   AbstrakTransformasi Laplace merupakan salah satu jenis transformasi integral yang memungkinkan digunakan untuk menyelesaikan persamaan diferensial linear orde dua homogen maupun non homogen. Transformasi Laplace Modifikasi diperoleh dengan melakukan penambahan koefisien melalui variabel yang sesuai pada persamaan Transformasi Laplace yang dinyatakan dalam bentuk =   dengan  dan merupakan fungsi kernel transformasi, serta  merupakan variabel transformasi untuk .  Terdapat beberapa penerapan persamaan diferensial, salah satunya yaitu pada model rangkaian listrik. Permasalahan yang seringkali menjadi kendala yaitu ketika menjumpai masalah nilai batas. Paper ini bertujuan untuk mendapatkan penyelesaian persamaan diferensial linear  pada model rangkaian listrik sederhana (RLC) yang dihubungkan secara seri, dengan menggunakan transformasi Laplace modifikasi. Hasil penelitian ini memberikan solusi persamaan diferensial linear orde dua yang berbentuk:                                                           Kata kunci: persamaan diferensial linear orde dua, rangkaian listrik, transformasi Laplace modifikasi

scholarly journals The study of heat transfer phenomena by using modified homotopy perturbation method coupled by Laplace transform

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1105-1115
Author(s):  
Uriel Filobello-Nino ◽  
Hector Vazquez-Leal ◽  
Agustin Herrera-May ◽  
Roberto Ambrosio-Lazaro ◽  
Victor Jimenez-Fernandez ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Non Linear ◽  
Linear Problems ◽  
Linear Differential

In this paper, we present modified homotopy perturbation method coupled by Laplace transform to solve non-linear problems. As case study modified homotopy perturbation method coupled by Laplace transform is employed in order to obtain an approximate solution for the non-linear differential equation that describes the steady-state of a heat 1-D flow. The comparison between approximate and exact solutions shows the practical potentiality of the method.

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